Question

If $a:b=3:1$ and $b:c=5:1$ then find the value of ${\left(\frac{a^3}{15b^{2}c}\right)}^3$.

Answer 1

Given

$\frac{b}{c}=\frac{5}{1}$

$\Rightarrow b=5c$

and

$\frac{a}{b}=\frac{3}{1}$

$\Rightarrow a=3b=3\times 5c=15c$

Now,

${\left(\frac{a^3}{15b^{2}c}\right)}^3={\left(\frac{(15c{)}^3}{15(5c{)}^{2}c}\right)}^3$

$={\left(\frac{{15}^3{c}^3}{15\times 5^2\times c^3}\right)}^3$

$={\left(\frac{{15}^3}{15\times 5^2}\right)}^3$

$={\left(\frac{15\times 15}{5\times 5}\right)}^3$

$=(3\times 3{)}^3$

$=9^3$

$=729$